Related papers: Superposition Enhanced Nested Sampling
Advances in techniques for thermal sampling in classical and quantum systems would deepen understanding of the underlying physics. Unfortunately, one often has to rely solely on inexact numerical simulation, due to the intractability of…
The Bouncy Particle Sampler (BPS) is a Monte Carlo Markov Chain algorithm to sample from a target density known up to a multiplicative constant. This method is based on a kinetic piecewise deterministic Markov process for which the target…
We review Skilling's nested sampling (NS) algorithm for Bayesian inference and more broadly multi-dimensional integration. After recapitulating the principles of NS, we survey developments in implementing efficient NS algorithms in practice…
Bayesian data analysis is widely used across many disciplines, and representative examples in materials science include spectral analysis and sparse modeling. In such applications, the underlying models often become complex and yield…
In performing a Bayesian analysis, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multi-modal or exhibit pronounced (curving) degeneracies.…
The main idea of nested sampling is to substitute the high-dimensional likelihood integral over the parameter space $\Omega$ by an integral over the unit line $[0,1]$ by employing a push-forward with respect to a suitable transformation.…
Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…
Biased sampling of collective variables is widely used to accelerate rare events in molecular simulations and to explore free energy surfaces. However, computational efficiency of these methods decreases with increasing number of collective…
Many inverse problems in nuclear fusion and high-energy astrophysics research, such as the optimization of tokamak reactor geometries or the inference of black hole parameters from interferometric images, necessitate high-dimensional…
Bayesian inference with nested sampling requires a likelihood-restricted prior sampling method, which draws samples from the prior distribution that exceed a likelihood threshold. For high-dimensional problems, Markov Chain Monte Carlo…
In this work, we present Enhanced Representation-Based Sampling (ERBS), a novel enhanced sampling method designed to generate structurally diverse training datasets for machine-learned interatomic potentials. ERBS automatically identifies…
This is an overview paper written in style of research proposal. In recent years we introduced a general framework for large-scale unconstrained optimization -- Sequential Subspace Optimization (SESOP) and demonstrated its usefulness for…
Recently, learned image compression has attracted considerable attention due to its superior performance over traditional methods. However, most existing approaches employ a single entropy model to estimate the probability distribution of…
We propose a modified maximum-entropy (MENT) algorithm for six-dimensional phase space tomography. The algorithm uses particle sampling and low-dimensional density estimation to approximate large sets of high-dimensional integrals in the…
Many approaches in the field of machine learning and data analysis rely on the assumption that the observed data lies on lower-dimensional manifolds. This assumption has been verified empirically for many real data sets. To make use of this…
We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally…
We propose a new technique for consistent estimation of the number and locations of the change-points in the structure of an irregularly spaced time series. The core of the segmentation procedure is the Ensemble Binary Segmentation method…
To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer…
This paper focuses on multi-block optimization problems over transport polytopes, which underlie various applications including strongly correlated quantum physics and machine learning. Conventional block coordinate descent-type methods for…
Model merging aims to integrate multiple task-specific fine-tuned models derived from a shared pre-trained checkpoint into a single multi-task model without additional training. Despite extensive research, task interference remains a major…